Global hypoellipticity and global solvability for vector fields on compact Lie groups

30 Sep 2019 Kirilov Alexandre de Moraes Wagner Augusto Almeida Ruzhansky Michael

We present necessary and sufficient conditions to have global hypoellipticity and global solvability for a class of vector fields defined on a product of compact Lie groups. In view of Greenfield's and Wallach's conjecture, about the non-existence of globally hypoelliptic vector fields on compact manifolds different from tori, we also investigate different notions of regularity weaker than global hypoellipticity and describe completely the global hypoellipticity and global solvability of zero-order perturbations of our vector fields... (read more)

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